Communications in Analysis and Geometry

Volume 16 (2008)

Number 4

Existence of outermost apparent horizons with product of spheres topology

Pages: 799 – 817

DOI: http://dx.doi.org/10.4310/CAG.2008.v16.n4.a3

Author

Fernando Schwartz (Duke University)

Abstract

In this paper we construct the first examples of $(n+m+2)$-dimensional asymptotically flat Riemannian manifolds withnon-negative scalar curvature that have outermost minimalhypersurfaces with non-spherical topology for $n,m\ge 1$.

The outermost minimal hypersurfaces are, topologically,$S^n\times S^{m+1}$. In the context of general relativitythese hypersurfaces correspond to outermost apparenthorizons of black holes.

Full Text (PDF format)